Preprint Article Version 1 This version is not peer-reviewed

On Extended Caputo Fractional Derivative Operator

Version 1 : Received: 27 December 2017 / Approved: 28 December 2017 / Online: 28 December 2017 (08:11:51 CET)

How to cite: Rahman, G.; Nisar, K.S.; Arshad, M.. On Extended Caputo Fractional Derivative Operator. Preprints 2017, 2017120195 (doi: 10.20944/preprints201712.0195.v1). Rahman, G.; Nisar, K.S.; Arshad, M.. On Extended Caputo Fractional Derivative Operator. Preprints 2017, 2017120195 (doi: 10.20944/preprints201712.0195.v1).

Abstract

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

Subject Areas

hypergeometric function; beta function; extended hypergeometric function; Mellin transform; fractional derivative; Caputo fractional derivative; Appell's function; generating relation

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